The run bettered the Kaizer Chiefs' 19-match streak in the 2014-2015 en route to becoming champions.
Victory near East London stretched Sundowns' six-point lead over second-place AmaZulu in the championship chase, and they have played two fewer matches due to CAF Champions League commitments.
The Pretoria club lost their first match of the 2020-2021 season last October, a knockout clash against Bloemfontein Celtic, and have since been unbeaten in 20 league matches and two FA Cup ties.
Themba Zwane put Sundowns ahead on 16 minutes by firing a penalty over the outstretched left hand of debutant Chippa goalkeeper Ismail Watenga from Uganda into the corner of the net.
Dominant Sundowns should have been further ahead before Chippa levelled on 49 minutes when Nigerian Augustine Kwem fired across Denis Onyango, another Ugandan goalkeeper, into the far corner.
Second-last Chippa threatened to score again through aerial strength off crosses and set pieces before Sundowns regained control, and the lead on 74 minutes.
Namibian Peter Shalulile reacted quickly and bravely to nod a rebound off the crossbar into the net from point-blank range for his 15th goal of the season in all competitions.
New Chippa coach Siyabulela Gwambi brought on Liberian veteran Anthony Laffor, a former Sundowns star, and Cameroonian Bienvenu Eva Nga, but neither could produce a second equaliser.
Defeat left Chippa, whose chairman Siviwe Mpengesi constantly changes coaches, just four points above bottom club Black Leopards with each having eight matches to play.
The club finishing last are automatically relegated and the second-last side go into play offs with two second-division teams for one Premiership place.
Standout matches today